Question: top-left: 5. Elena wanted to find the slope and y-intercept of the graph of $$25x - 20y = 100$$. She decided to put the equation in slope-intercept form first. Here is her work:
center: $$25x - 20y = 100$$
$$20y = 100 - 25x$$
$$y = 5 - \frac{5}{4} x$$
bottom-left: She concluded that the slope is $$-\frac{5}{4}$$ and the y-intercept is $$(0,5)$$.User: a- what was elena's mistake? b- explain reasoning in about 15 words
1. **State the problem:** Find the slope and y-intercept of the line given by $$25x - 20y = 100$$.
2. **Rewrite the equation in slope-intercept form $$y = mx + b$$:**
Start with $$25x - 20y = 100$$.
Subtract $$25x$$ from both sides:
$$-20y = 100 - 25x$$
Divide both sides by $$-20$$:
$$y = \frac{100 - 25x}{-20}$$
3. **Simplify the right side:**
$$y = \frac{100}{-20} - \frac{25x}{-20} = -5 + \frac{25}{20}x$$
Simplify $$\frac{25}{20} = \frac{5}{4}$$:
$$y = -5 + \frac{5}{4}x$$
4. **Identify slope and y-intercept:**
Slope $$m = \frac{5}{4}$$
Y-intercept $$b = -5$$
5. **Elena's mistake:** She forgot to divide the $$100$$ by $$-20$$ correctly and wrote $$5$$ instead of $$-5$$.
6. **Reasoning in about 15 words:**
Dividing $$100$$ by $$-20$$ gives $$-5$$, not $$5$$; sign error caused wrong intercept.
**Final answer:**
Slope is $$\frac{5}{4}$$ and y-intercept is $$(0,-5)$$, not $$(0,5)$$.